From fig:S8 we observe two things. For CMB and CMB+Pantheon, the estimated values of the \(S_8\)  parameter in all the extended cosmological scenarios are very far from both KIDS-1000 [1]} and DES-Y3 [2]}, when they assume a vanilla \(\Lambda \) CDM model.Both KiDS-100 and DES collaborations explored extended scenarios in Refs. [3]}, [4]}, but the combinations of parameters explored here are not considered, so we can't make a safe comparison. Moreover, they are also far from Planck's estimation assuming a vanilla \(\Lambda \) CDM model, except in the extended scenarios assuming a cosmological constant, where for CMB+Pantheon case \(S_8\)  values are slightly close to it. For all the other cases, for these two datasets the tension in the \(S_8\)  parameter increases significantly. This is because of the indication for a closed Universe coming from these two datasets when it is not assumed a cosmological constant.
On the other hand, when we look at the estimations of \(S_8\)  by CMB+BAO and CMB+BAO+Pantheon, we see that these estimations are almost similar to the Planck values assuming a vanilla \(\Lambda \) CDM model.
This indicates that within such extended scenarios, the \(S_8\)  tension increases when there is an indication for a closed Universe.
